Spin echo

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Spin echo: Pulse sequence (above) and Signal (below)

In nuclear magnetic resonance, spin echo refers to the refocusing of precessing nuclear spin magnetisation by a 180° pulse of resonant radiofrequency.

The NMR signal observed following an initial excitation pulse (orange in diagram) decays with time due to both spin-spin relaxation and any inhomogeneous effects which cause different spins to precess at different rates e.g. a distribution of chemical shifts or magnetic field gradients. Relaxation leads to an irreversible loss of magnetisation (decoherence), but the inhomogeneous dephasing can be reversed by applying a 180° or inversion pulse (blue in diagram) that inverts the magnetisation vectors. If the inversion pulse is applied after a period T of dephasing, the inhomogeneous evolution will rephase to form an echo at time 2T. The intensity of the echo relative to the initial signal is given by $exp( - 2 T / T 2)$ where $T 2$ is the time constant for spin-spin relaxation.

Another method for generating spin echoes is to apply three successive 90° pulses. After the first 90° pulse, the magnetization vector is exchanging energy through dipole, dipole interactions and in a time τ, forms what is often referred to as a “pancake” in the x’-y’ plane. A further 90° pulse is then applied such that our “pancake” is now in the x’-z’ plane. When considering the two types of relaxation, spin – lattice and spin – spin (T1 and T2) we assume the first to take an infinite amount of time as such allowing the spin vectors to precess about the z axis. Now, the angle each spin makes with the z’ axis is equal to the angle it previously made about the y’ axis. At this point any change in angle that now takes place will require a change in energy thus implying a spin – lattice interaction is necessary. This implies a permanent memory of the state of the system as it was at time τ. After a further time τ2 a third pulse is applied and our Magnetization vector is back in the x’ – y’ plane and will lie in the same direction as for a (90 – τ – 180) spin echo sequence formally discussed. Then after final delay of τ we see what is commonly referred to as a stimulated echo. This technique is commonly used when studying T1 relaxation times. This is because by measuring the magnitude of the correct echo and its decay with pulse width separation we can determine T1. The echo magnitude will depend on the relation, exp(-τ2/T1).

Echo phenomena are important features of coherent spectroscopy which have been observed and used in various fields from magnetic resonance to laser spectroscopy. They are fundamental to magnetic resonance imaging. Echoes were first detected in nuclear magnetic resonance by Erwin Hahn in 1950^[1].